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Astrophysics Part 2 2012

1.
ASTROPHYSICS E2Stellar Radiation & Stellar Types

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Stars Stars are formed by interstellar dust coming together through mutual gravitational attraction. The loss of potential energy is responsible for the initial high temperature necessary for fusion. The fusion process releases so much energy that the pressure created prevents the star from collapsing due to gravitational pressure.

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Nuclear fusion Very high temperatures are needed in order to begin the fusion process: usually 107 K. Fusion Applet

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2 2 41 H + H 1 2 He + 25 MeV Must overcome the coulomb (electrostatic) repulsion between the nuclei so that they can fuse together. In Stable Stars there is an equilibrium between the gravitational attraction of all of the gas and dust particles and… … the outward pressure exerted by the nuclear fusion process. This keeps a stable star from collapsing or exploding.

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A star is a big ball of gas, with fusion going on at its center, held together by gravity! Massive Sun-like Low-mass Star Star StarThere are variations between stars, but by and large they’re really pretty simple things.

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What is the most importantthing about a star? MASS! The mass of a normal star almost completely determines itsLUMINOSITY and TEMPERATURE! Note: “normal” star means a star that’s fusing Hydrogen into Helium in its centre (we say “hydrogen burning”).

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The LUMINOSITY of a star isthe TOTAL ENERGY emitted pertime from the surface of the star: This light bulb has a luminosity of 60 Watts The energy the Sun emits is generated by the fusion in its core…

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What does luminosity have to dowith mass?The mass of a star determines Pressurethe pressure in its core: Gravity pulls outer layers The core in, supports the Gas Pressure pushes weight of the them out. whole star!The more mass the star has,the higher the central pressure!

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Luminosity is an intrinsic property…it doesn’t depend on distance! This light bulb has a luminosity of 60 Watts… …no matter where it is, or where we view it from, it will always be a 60 Watt light bulb.

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LuminosityThe Luminosity of a star is the energy that it releasesper second. Our Sun has a luminosity of 3.90x1026 W(often written as L): it emits 3.90x1026 joules persecond in all directions.The energy that arrivesat the Earth is only avery small amountwhen compared will thetotal energy released bythe Sun.

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TOK The ancient Greeks classified stars by their brightness using the naked eye. They were quite good at it. Have we lost skills because of our reliance on technology? Is this a concern?

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Apparent brightness When the light from the Sun reaches the Earth it will be spread out over a sphere of radius d. The energy received per unit time per unit area is b, where: L b 2 d 4 d b is called the apparent brightness of the star

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Apparent brightness The apparent brightness is directly proportional to the star’s luminosity and varies as the inverse square of the stars distance.

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LuminosityQuestionThe Sun is a distance d=1.5 x 1011 m from the Earth.Estimate how much energy falls on a surface of 1m2in a year. L= 3.90x1026 W d

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Black body radiation A black body is a perfect emitter. A good model for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum. There is a clear relationship between the temperature of an object and the wavelength for which the emission is maximum. That relationship is known as Wien’s law: maxT constant -3 maxT 2.9x10 m K

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Black body radiation Apart from temperature, a radiation spectrum can also give information about luminosity. The area under a black body radiation curve is equal to the total energy emitted per second per unit of area of the black body. Stefan showed that this area was proportional to the fourth power of the absolute temperature of the body. The total power emitted by a black body is its luminosity. According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by: L σAT 4 where, σ = 5.67x108 W m-2 K-4 , A = 4πr2

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Why is this important? The spectrum of stars is similar to the spectrum emitted by a black body. We can therefore use Wien Law to find the temperature of a star from its spectrum. If we know its temperature and its luminosity then its radius can be found from Stephan-Boltzmann law.

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Example 1 The apparent brightness of our Sun is 1,393 Wm-2. This can be determined using light sensors on Earth. We know that the Earth is 1AU from the Sun. The Sun has an approximate black body spectrum with most of the energy radiated at a wavelength of 5.0 X 10-7 m. This is done using a spectrometer on Earth.

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Example 1 Use the above information to find out the  1. Luminosity of the Sun  2. Surface temperature of the Sun  3. Radius of the Sun  USE YOUR DATA BOOKLET!

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Atomic Spectra The spectrum of atomic hydrogen was discussed and accounted for using the Bohr model of the atom. Remember that the electron shells of a given atom can absorb a specific frequency of energy.  E = hf Lets look at Hydrogen as an example.

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Atomic Spectra An electron transition downwards leads to an emission of a specific frequency of light. This produces an emission spectrum if observed through a spectrometer.

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Atomic Spectra Another good example of line emission spectra is the burning of sodium. The gaseous sodium’s electrons produce two distinct spectral lines in the yellow region of the E-M spectrum.

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Atomic Spectra A particular gas, like Hydrogen can also ABSORB specific frequencies of light. This removes particular frequencies from a continuous spectrum. This is called an ABSORPTION SPECTRUM.

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Atomic Spectra In all cases the absorption and the emission spectra will match perfectly.

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Atomic Spectra The spectrum seen from a star is due to the presence of a particular chemical element in the outer atmosphere of the star. The sun produces absorption lines of Hydrogen, iron, calcium and sodium.

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Atomic Spectra The absorption spectrum also tells us the outer temperature of the sun’s surface. For every element there is a temperature range which will produce strong absorption lines.

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Atomic Spectra Examples would be…  Hydrogen absorption lines occur at temperatures of 4000 to 12 000 K.  Helium lines require temperatures of between 15 000 and 30 000 K in order to get their electrons to absorb energy.

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Atomic Spectra Different atoms are sensitive to different temperatures. It is possible to determine a star’s temperature by the absorption spectra that the star is producing.

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Atomic Spectra The chemical composition of stars due to their line absorption spectra are found to be remarkably similar. The average composition of stars is 74% Hydrogen, 25% Helium and only 1% other elements.

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Atomic Spectra In summary, line absorption spectra tell us more about a star’s temperature rather than its chemical composition (as most stars have the same composition).

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Stars can be arranged intocategories based on thefeatures in their spectra… This is called “Spectral Classification” How do we categorise stars? A few options: 1. by the “strength” (depth) of the absorption lines in their spectra 2. by their color as determined by their blackbody curve 3. by their temperature and luminosity

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First attempts to classify stars used the strength of their absorption lines… Stars were labeled “A, B, C…” in order of increasing strength of Hydrogen lines. They also used the strength of the Harvard “computers”! Williamina Fleming

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Eventually, the connection was made between the observables and the theory. Observable: • Strength of Hydrogen Absorption Lines • Blackbody Curve (Color) Theoretical: • Using observables to determine things we can’t measure: Temperature and LuminosityCecilia Payne

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The Hertzsprung-Russell diagram This diagram shows a correlation between the luminosity of a star and its temperature. The scale on the axes is not linear as the temperature varies from 3000 to 25000 K whereas the luminosity varies from 10-4 to 106, 10 orders of magnitude.

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H-R diagram  The stars are not randomly distributed on the diagram.  There are 3 features that emerge from the H-R diagram:  Most stars fall on a strip extending diagonally across the diagram from top left to bottom right. This is called the MAIN SEQUENCE.  Some large stars, reddish in colour occupy the top right – these are red giants (large, cool stars).  The bottom left is a region of small stars known as white dwarfs (small and hot)